It's really up to the GM. Personally, I aim for half of the PL and PP of the original character. Occasionally, that results in lower-ranked powers sticking around. In a few cases, such as Magical Pretty Princess Loli-Chan, the Normal Identity had skills and feats that the transformed side did not have.

One would be the Bruce Banner/Incredible Hulk version. Banner is very different than the Hulk, but much lower in PL and cost.

Then you have the Normal ID where the person is essentially the same only without powers. Superman has a Normal Id under Red Sun. Tony Stark has a Normal Id without his armor. (Yes that qualifies because he has two identities, unlike someone with a Magic Necklace who can go around in super form all the time).